Three layers is an awful idea. Whoever that guy is, he isn't sure what he is doing. A vpn will provide you with weak privacy. That's it's job. It will not provide you with strong anonymity. It's not going to protect you against any competent government adversary.
A VPN is not a solution for anonymity. It's for privacy only. The base solution in all my solutions is always VPN => Tor (exactly as how the Grugq explains). You make the Tor connection first, and then VPN though that.
This solution is great, and would work for most people. But keep in mind that your ISP knows you are using Tor. If you live in the middle of nowhere you might be the only person within a 50-100 mile radius using Tor. This is absolutely shit. Many people associate Tor with criminal acivity the same way people think bitcoins are used to only buy drugs. Go ahead, ask strangers if they heard of Tor and what they know baout it.
Your ISP likely thinks the same. While they might not do anything because Tor is not illegal, I can assure you they know. If the FBI or whoever is interested asking the ISP who used Tor between the times of XYZ because they are investigating some crime, you're automatically added to that list.
More people use VPNs than Tor, so you want to keep your Tor traffic hidden from your ISP and blend in with the general population.
VPN after Tor - similar problems. You have just gotten yourself a permanent exit node.
As the Grugq said: TOR to VPN – ok; VPN to TOR – go to jail
Connect to Tor first, then connect to the VPN.
Of course you have a permanent exit node in what he says is "okay", but the source of your VPN connection is always random. Your VPN does not know who you are. Now, you can give yourself away by not obeying the first rule of opsec: "STFU". But you'd give yoruself away with a Tor-only solition by doing the same.
Why is "VPN to TOR – go to jail"? Easy. This is equivalent to a Tor-only solution. You are still vulnerable to correlation attacks AND malicious Tor exit nodes. All you are doing hiding original location from the Tor entry node.